| Abstract: |
| In many PDEs models some constraints need to be imposed when considering concrete applications. This is for instance the case of evolutionary systems (such as heat conduction, transportation networks, population dynamic, etc.) where realistic models must incorporate the consideration that the state should adhere to some positivity constraints to ensure their physical relevance.
In this talk, we discuss the positivity property of linear evolution systems. We present criteria for well-posedness, positivity and stability of a class of infinite-dimensional systems. These criteria are based on an inverse estimate with respect to the Hille-Yosida Theorem. This unifies previous results available in the literature and that were established separately so far. As for illustration, we exhibit the feasibility of these criteria through a structured population model with (unbounded) delay in the birth process. |
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